If \(A=\{0,1,2,3\}\), in all subsets of A, how many times will the element 0 appear in total?
Answer and explanation
Correct answer: 8
A has four elements. To form a subset that contains the fixed element 0, we only decide independently whether each of the other three elements, 1, 2, and 3, is included or excluded. Each has two choices, so the number of subsets containing 0 is \(2\times2\times2=2^3=8\). Thus 0 appears in eight subsets in total. The number 16 is the total number of all subsets of A, including those that do not contain 0.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
A has four elements. To form a subset that contains the fixed element 0, we only decide independently whether each of the other three elements, 1, 2, and 3, is included or excluded. Each has two choices, so the number of subsets containing 0 is \(2\times2\times2=2^3=8\). Thus 0 appears in eight subsets in total. The number 16 is the total number of all subsets of A, including those that do not contain 0.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
